Let q_i denotes commodity I and p_i is the price of that commodity. Let y denotes money income of the consumer. Suppose v_i = p_i/y. The budget constraint written as:

n

1 =∑ v_iq_i (1)

i=1

Since optimal solutions in the demand functions are homogeneous of degree zero in income and prices, nothing essential is lost by this transformation to ‘normalised’ prices. The utility function U = f(q₁,q_n) together with equation (1) gives the following first order conditions of utility maximization:

f_i – λv_i = 0 for all I – 1,….n

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